Home/Chain Registry/Block #353,250

Block #353,250

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/10/2014, 8:04:23 PM · Difficulty 10.3227 · 6,448,537 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

b3ff8ea4ede02e15c8164cd9bb65704158f2702b4b9c142582d0f5e99d0112b2

View on Chainz ↗

Height

#353,250

Difficulty

10.322709

Transactions

Size

209 B

Version

Bits

0a529d09

Nonce

56,230

Timestamp

1/10/2014, 8:04:23 PM

Confirmations

6,448,537

Merkle Root

320801f79e8bd3a9bdad8a8701e5ec0a9ae565f61216508607d91c3da6af5276

Transactions (1)

Coinbase320801f79e8bd3…d91c3da6af5276

1 in → 1 out9.3700 XPM116 B

AbwWkWZt…kawDhufa

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.554 × 10¹⁰¹(102-digit number)

25545058255644602406…30662615749583910400

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.554 × 10¹⁰¹(102-digit number)

25545058255644602406…30662615749583910399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.554 × 10¹⁰¹(102-digit number)

25545058255644602406…30662615749583910401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.109 × 10¹⁰¹(102-digit number)

51090116511289204812…61325231499167820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.109 × 10¹⁰¹(102-digit number)

51090116511289204812…61325231499167820801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.021 × 10¹⁰²(103-digit number)

10218023302257840962…22650462998335641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.021 × 10¹⁰²(103-digit number)

10218023302257840962…22650462998335641601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.043 × 10¹⁰²(103-digit number)

20436046604515681925…45300925996671283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.043 × 10¹⁰²(103-digit number)

20436046604515681925…45300925996671283201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.087 × 10¹⁰²(103-digit number)

40872093209031363850…90601851993342566399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.087 × 10¹⁰²(103-digit number)

40872093209031363850…90601851993342566401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 353250

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock b3ff8ea4ede02e15c8164cd9bb65704158f2702b4b9c142582d0f5e99d0112b2

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #353,250 on Chainz ↗